XV. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another. BOOK I. XVI. And this point is called the centre of the circle. XVII. A diameter of a circle is a straight line drawn through the See N. centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the "A segment of a circle is the figure contained by a straight XX. Rectilineal figures are those which are contained by straight lines. Trilateral figures, or triangles, by three straight lines. XXI. XXII. XXIII. Quadrilateral, by four straight lines. Multilateral figures, or polygons, by more than four straight lines. XXIV. Of three-sided figures, an equilateral triangle is that which has three equal sides. XXV. An isosceles triangle is that which has only two sides equal. Boox I. ΔΔΔ XXVI. A scalene triangle, is that which has three unequal sides. A right angled triangle, is that which has a right angle. An obtuse angled triangle, is that which has an obtuse angle. XXIX. л An acute angled triangle is that which has three acute angles. Of four-sided figures, a square is that which has all its sides XXXI. An oblong, is that which has all its angles right angles, but has not all its sides equal. XXXII. A rhombus, is that which has its sides equal, but its angles are not right angles. XXXIII. See N. A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles. XXXIV. All other four-sided figures besides these, are called Trapeziums. XXXV. Parallel straight lines, are such as are in the same plane, and which, being produced ever so far both ways, do not meet. BOOK I. POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre, at any distance from that centre. A X IOM S. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. N. B. 'When several angles are at one point B, any one ' of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is, at the point in 'which the straight lines that contain the angle meet one another, is put between the other two letters, and one of 'these two is somewhere upon one of those straight lines, ' and the other upon the other line: Thus the angle which is contained by the straight lines AB, CB, is named the angle ABC, or CBA; that which is contained by AB, BD, 'is named the angle ABD, or DBA; and that which is 'contained by BD, CB, is called the angle DBC, or CBD; but, if there be only one angle at a point, it may be expressed by a letter placed at that point; as the angle at E.' X. When a straight line standing on ano- it. XI. An obtuse angle is that which is greater than a right angle. XII. An acute angle is that which is less than a right angle. XIII. "A term or boundary is the extremity of any thing." XIV. A figure is that which is inclosed by one or more boundaries. XV. Book I. XVI. And this point is called the centre of the circle. XVII. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight "line, and the circumference it cuts off." XX. Rectilineal figures are those which are contained by straight lines. Trilateral figures, or triangles, by three straight lines. XXI. Multilateral figures, or polygons, by more than four straight lines. XXIV. Of three-sided figures, an equilateral triangle is that which has three equal sides. XXV. An isosceles triangle is that which has only two sides equal. |